Atlas518 of 3,942

I.A.128

m₃ = 0.5

From Li, Jing & Liao (2018)

I.A.128 m₃ = 0.5 is a periodic orbit of the planar three-body problem: three masses in the ratio 1 : 1 : 0.5 that return to their starting positions and velocities every 128.61 time units, published by Li, Jing & Liao (2018). Class I.A orbits found with Liao’s clean numerical simulation method, for a third body of varying mass. It is weakly unstable (largest Floquet multiplier 6.577), so a small nudge makes it unravel over a few periods. The bodies pass within 0.000281 of each other at a top speed of 68.9, line up 270 times a period, and the computed loop closes to 9.1×10⁻²⁵.

Measured over one period

Period: 128.6102392
Masses: 1 : 1 : 0.5
Energy: -1.36160
Angular momentum: 0
Closest approach: 2.8×10⁻⁴
Top speed: 68.86
Path length: 336.73
Alignments per period: 270
Topology: aabAbaBAbaBAbaBAbaBAbbAABaBBaabAbaBAbaBAbaBAbaBAbbAABaBBaabAbaBABaBAbaBAbaBAbbAAbaBBaabAbbAABaBAbaBAbaBAbaBAbaBBaabAbbAABaBAbaBAbaBAbaBAbaBBaabAbbAABaBAbabAbaBAbaBAbaBBaaBAbbAABaBB (free-group class)
Stability: weakly unstable (|λ|max 6.577)
Loop closure: 9.1×10⁻²⁵

Neighbours on the map

All I.A orbits, the families of periodic three-body orbits, or the atlas map.